0. Math Review

1. Intro to Physics Units

2. 1D Motion / Kinematics

3. Vectors

4. 2D Kinematics

5. Projectile Motion

6. Intro to Forces (Dynamics)

7. Friction, Inclines, Systems

8. Centripetal Forces & Gravitation

9. Work & Energy

10. Conservation of Energy

11. Momentum & Impulse

12. Rotational Kinematics

13. Rotational Inertia & Energy

14. Torque & Rotational Dynamics

15. Rotational Equilibrium

16. Angular Momentum

17. Periodic Motion

18. Waves & Sound

19. Fluid Mechanics

20. Heat and Temperature

21. Kinetic Theory of Ideal Gases

22. The First Law of Thermodynamics

23. The Second Law of Thermodynamics

24. Electric Force & Field; Gauss' Law

25. Electric Potential

26. Capacitors & Dielectrics

27. Resistors & DC Circuits

28. Magnetic Fields and Forces

29. Sources of Magnetic Field

30. Induction and Inductance

31. Alternating Current

32. Electromagnetic Waves

33. Geometric Optics

34. Wave Optics

36. Special Relativity

[BOOK PHYS] !CLUTCH

You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. (a) How much time does it take the pendulum bob to reach its highest speed?

A pendulum is made by tying a 75 g ball to a 130-cm-long string. The ball is pulled 5.0° to the side and released. How many times does the ball pass through the lowest point of its arc in 7.5 s?

A wooden meter stick is suspended from one end with a frictionless peg. If the meter stick is given a small bump and allowed to oscillate as a pendulum, what is the period of motion?

A 20 kg child is on a swing that has chains <math display='inline'><mrow><mn>2</mn><mo>.</mo><mrow><mn>4</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math> long. At what frequency should the child's father deliver his pushes to ensure the highest swing possible?

Simple Pendulum - Simple Harmonic Motion Derivation using Calculus

When is a Pendulum in Simple Harmonic Motion?(SHM)

A uniform rod of mass M and length L swings as a pendulum on a pivot at distance L/4 from one end of the rod. Find an expression for the frequency f of small-angle oscillations.

You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. (b) How much time does it take if the pendulum is released at an angle of 1.75° instead of 3.50°?

A certain simple pendulum has a period on the earth of 1.60 s. What is its period on the surface of Mars, where g = 3.71 m/s^2?

A building in San Francisco has light fixtures consisting of small 2.35-kg bulbs with shades hanging from the ceiling at the end of light, thin cords 1.50 m long. If a minor earthquake occurs, how many swings per second will these fixtures make?

Simple Harmonic Motion (1 of 16): Period of a Pendulum

Simple Harmonic Motion of Pendulums

simple harmonic motion - the pendulum

A 20 kg child is on a swing that has chains <math display='inline'><mrow><mn>2</mn><mo>.</mo><mrow><mn>4</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math> long. Being interested in physics, the child's father gives a push and then watches to see what happens. He notices that the amplitude of the child's oscillation decreases by half in 20 s. What is the value of the time constant?

Astronauts on the first trip to Mars take along a pendulum that has a period on earth of 1.50 s. The period on Mars turns out to be 2.45 s. What is the free-fall acceleration on Mars?

Example

8.01x - Module 15.09 - Simple harmonic motion of pendulum.

A pendulum on a 75-cm-long string has a maximum speed of 0.25 m/s. What is the pendulum's maximum angle in degrees?

A 15-cm-long, 200 g rod is pivoted at one end. A 20 g ball of clay is stuck on the other end. What is the period if the rod and clay swing as a pendulum?

Pendulum Equations

Anderson Video - Pendulum Mechanics

A uniform rod of length L oscillates as a pendulum about a pivot that is a distance x from the center.

a. For what value of x, in terms of L, is the oscillation period a minimum?

Simple Harmonic Motion (2 of 16): Pendulum, Calculating Period, Frequency, Length and Gravity

Anderson Video - The Mysterious Wave Pendulum

Interestingly, there have been several studies using cadavers to determine the moments of inertia of human body parts, information that is important in biomechanics. In one study, the center of mass of a 5.0 kg lower leg was found to be 18 cm from the knee. When the leg was allowed to pivot at the knee and swing freely as a pendulum, the oscillation frequency was 1.6 Hz. What was the moment of inertia of the lower leg about the knee joint?

A simple pendulum 2.00 m long swings through a maximum angle of 30.0° with the vertical. Calculate its period (a) assuming a small amplitude, and (b) using the first three terms of Eq. (14.35). (c) Which of the answers in parts (a) and (b) is more accurate? What is the percentage error of the less accurate answer compared with the more accurate one?

Simple Pendulum in Harmonic Motion

The historic first playground on Mars has just opened. A child is on a swing with chains of length <math display='inline'><mrow><mn>2</mn><mo>.</mo><mrow><mn>3</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow><mo>.</mo></mrow></math> If a parent pulls the child backward <math display='inline'><mrow></mrow></math> from equilibrium, what is the child's maximum speed? The acceleration due to gravity on Mars is <math display='inline'><mrow><mn>3.7</mn><msup><mrow><mtext>&#x00A0;</mtext><mtext>m/s</mtext></mrow><mn>2</mn></msup></mrow></math>.

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